Teaching

 

Summer Semester 2025

Functional Analysis / Operator Theory

The two main topics of this course are abstract spectral theory and Schatten classes. In the first part, we will study commutative C*-algebras, culminating in the Gelfand representation theorem. In the second part, our focus lies on certain classes of bounded operators on Hilbert space that are related to the trace, namely trace-class operators, Hilbert-Schmidt operators etc. All these operators are compact, so we will also look into this broader class a bit. Additionally, I also plan to include some fundamentals of functional analysis that were not covered in Mathematical Physis 2, namely the Hahn-Banach theorem and the Stone-Weierstraß theorem.

In the seminar, we will look at properties of entropy in quantum information. Topics for talks include quantum states and quantum channels, quantum Stein lemma and Uhlmann's monotonicity theorem (also known as data processing inequality).

Required background is a solid understanding of functional analysis as covered in the course Mathematical Physics 2. If you did not take this course with me, have a look at Chapter 4 of the Lecture Notes posted below.

Notes:

These notes will be updated as the course progresses: Lecture Notes

Literature:

Time:

Thursday 11:00 - 13:00 (SG 312), Friday 9:00 - 11:00 (SG214)

Winter Semester 2024/25

Mathematical Physics 1 and 2

This is the introductory course for the master's program Mathematical Physics, taught jointly with Prof. Gajic (ITP). The mathematics part will cover a bit of everything, ranging from metric spaces and multivariate analysis (Banach fixed-point theorem, inverse and implicit function theorem) over manifolds and integration of differential forms (Stokes's theorem) and measure and integration theory (convergence theorems for the Lebesgue integral) to operator theory on Hilbert space and spectral theory (spectral theorem for unbounded self-adjoint operators).

This course is administered via moodle.

Literature:

  • Lecture Notes
  • Amann, Escher. Analysis 1 - 3
  • Reed, Simon. Methods of Modern Mathematical Physics I
  • Teschl. Mathematical Methods of Quantum Mechanics

Time:

Lectures: Monday, Tuesday 11:00 - 13:00, Thursday, Friday 9:00 - 11:00
Recitations: Tuesday 15:00 - 17:00, Thursday 11:00 - 13:00

Winter Semester 2023/24

Trace inequalities and quantum entropies

Course at University of Paderborn

Lecture Notes

Winter Semester 2022/23

Linear Algebra for Life Scientists

Course at ISTA

Summer Semester 2022

Trace inequalities and quantum entropies

Course at ISTA, jointly taught with Haonan Zhang

Courses as Teaching Assistant

I taught the recitations for the following courses at the University of Jena (in German):
  • Winter 2019/2020 Analysis III
  • Winter 2015/2016 Functional Analysis II
  • Summer 2015 Ordinary Differential Equations
  • Summer 2013 Functional Analysis I
  • Winter 2012/2013 Analysis III
  • Summer 2012 Analysis II

Supervision

I co-supervised the following student theses at the University of Jena together with Daniel Lenz
  • Timon Weinmann, Bachelor’s thesis on Self-adjoint realizations of Hamiltonians of coupled systems, Jena, 2019
  • Sebastian Uschmann, Master’s thesis on Cohomology of Dirichlet forms, Jena, 2018